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Simplifying 40x2 + -25x = -3 Reorder the terms: -25x + 40x2 = -3 Solving -25x + 40x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + -25x + 40x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -25x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.075 + -0.625x + x2 = 0 Move the constant term to the right: Add '-0.075' to each side of the equation. 0.075 + -0.625x + -0.075 + x2 = 0 + -0.075 Reorder the terms: 0.075 + -0.075 + -0.625x + x2 = 0 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + -0.625x + x2 = 0 + -0.075 -0.625x + x2 = 0 + -0.075 Combine like terms: 0 + -0.075 = -0.075 -0.625x + x2 = -0.075 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = -0.075 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = -0.075 + 0.09765625 Combine like terms: -0.075 + 0.09765625 = 0.02265625 0.09765625 + -0.625x + x2 = 0.02265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 0.02265625 Calculate the square root of the right side: 0.150519932 Break this problem into two subproblems by setting (x + -0.3125) equal to 0.150519932 and -0.150519932.Subproblem 1
x + -0.3125 = 0.150519932 Simplifying x + -0.3125 = 0.150519932 Reorder the terms: -0.3125 + x = 0.150519932 Solving -0.3125 + x = 0.150519932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 0.150519932 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.150519932 + 0.3125 x = 0.150519932 + 0.3125 Combine like terms: 0.150519932 + 0.3125 = 0.463019932 x = 0.463019932 Simplifying x = 0.463019932Subproblem 2
x + -0.3125 = -0.150519932 Simplifying x + -0.3125 = -0.150519932 Reorder the terms: -0.3125 + x = -0.150519932 Solving -0.3125 + x = -0.150519932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -0.150519932 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.150519932 + 0.3125 x = -0.150519932 + 0.3125 Combine like terms: -0.150519932 + 0.3125 = 0.161980068 x = 0.161980068 Simplifying x = 0.161980068Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.463019932, 0.161980068}
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